1 Parameterisation specific for lameness Parameterisation: - - PDF document

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Case Exam ple I I

Sim herd: Advanced Herd Managem ent Jehan Ettem a Economic decision making on prevention and control of clinical lameness in Danish dairy herds

Case Example:

• introduction
• material and methods
• results
• sensitivity analysis
• costs of lameness
• effect of treatments
• discussion
• representative
• usable in practice
• other applications

Introduction

Harris et al. (1988)

DKK 195

Whitaker et al. (1983)

DKK 500

Enting et al. (1997)

DKK 775

McCluggage et al. (1985)

DKK 1574

Kossaibati et al. (1997)

DKK 2931

Material and methods

SimHerd III (Østergaard et al. 2003)

• stochastic
• dynamic
• mechanistic

Common strategy of working with Simherd

• 1. Formulate treatments, strategies and scenarios: ”what if...”
• 2. Parameterisering: risk factors, effects, design of your farm
• literature study
• field study
• both emperical and normative knowledge
• 3. Programming, if necessary (new disease)
• 4. Validation: sensitivity analysis
• 5. Run of the actual simulations
• 6. Analize and interpret the results

Parameterisation: definition of the State of Nature ”complete set of model input parameters”

Biological variables Reproduction strategy Replacement strategy Drying-off strategy Prices Mortality Start breeding heifers Max days open Yield at drying off Milk price 5% 14 mo. 427 5,0 Liter

DKK 2,20

General production and management system of modern Danish dairy herd

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Parameterisation: definition of the State of Nature Modern Danish dairy herd

• Herdsize: 120 cows
• Milk yield level: 8500 kg ECM
• 2 kinds of roughage and concentrates
• Minimum length dry period: 49 days
• Involuntary culling: 18-20%
• Stillbirths: 11% (1. parity) and 6% (older)
• Heat detection efficiency: 50%
• Feeding of milk replacer
• Common incidence of diseases (e.g. mastitis 25%, DA 1.4%)

Parameterisation specific for lameness

Risk factors, effect parameters, interrelations

Difficulties with respect to lameness: Lameness is a symptom of several diseases:

Digital dermatitis Sole Ulcer White line disease Interdigital Hyperplasia Sole bruising ...

Parameters: result of weighted average of values found in literature for dermatitis, sole ulcer...

25% of the lameness causes 21% 17% 7% 8% Risk factor Base risk 0,16 Cow specific risk factors Parity 1 vs. 3, OR 0,56 Parity 2 vs. 3, OR 0,78 Parity 4 vs. 3, OR 1,25 Milk yield potential, OR per kg 1,08 Lactational recurrence, OR 2,31 High risk season, day Sept-May High risk season vs. Remaining year, OR 1,840 Risk of lameness in the third lactation for a herd-average producing cow without previous cases of any disease Cow specific risk: logistic regression model logit value

• base risk

0,16

• 1,66
• parity 2

OR 0,78

• 0,25
• milk yield potential + 1 kg

OR 1,08 0,08

• december (high risk)

OR 1,84 0,61

1 P(123) = ------------------------------ 1+e-(β0+βpartiy+βmilk yield + βseason) 1 P(123) = ------------------------------ = 0,22 1+e-(-1,66 + -0,25 + 0,08 + 0,61)

Cow specific risk: logistic regression model Triggering of the occurence of lameness Draw a sample from a uniform distribution around P = 0,22 X = cow becomes lame

1 P(123) = ------------------------------ = 0,22 1+e-(-1,66 + -0,25 + 0,08 + 0,61)

Lactation stage, time of occurence Gamma distribution (2,60) (α,β)

1 2 3 4 5 6 7 8 9 10 11 12

months of lactation

25 20 15 10 5

Incidence

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Effect parameters

Reduced milk yield 0,937 Duration in days 147 Daily weight loss, ratio of current weight 0,110 Duration in days 35 Reduced feed intake, ratio 0,960 Duration in days 35 Reduced conception rate, OR 0,78 Duration in days 147 Euthanised or died, ratio of lame cows 0,035

Effect parameters

Milk yield, feed intake, body weight

5 10 15 20 25 30 35 40

1 5 9 13 17 21 25 29 33 37 41 weeks after calving Kg ECM and SFU 520 540 560 580 600 620 640 Kg Body Weigth

milk yield feed intake body weight

SimCow: simulation of the production of an individual cow as a function of a certain production strategy

• mimic interaction between milk loss, feed intake and bodyweigth

Effect parameters

Treatment costs Each case of lameness is treated 1.4 times In 80% of the cases the trimmer/veterinarian treats the cows Kossaibati and Esslemont 1997

• interdigital lameness: 332 DKK
• sole ulcer:

700 DKK Zeddies et al. 1997 Mild case: 223 DKK Severe case: 543 DKK This study: 400 DKK per lameness cases (treated 1.4 times)

Design of ”what if” scenarios

• preventive measures, management strategies

Preventive trimming Footbaths Increase the access to pasture Rubber covering of concrete floors ...imagination

Recurring difficulty with respect to lameness: Efficacy of measures only for certain diseases footbaths infectious diseases rubber floors trauma related diseases

Design of ”what if” scenarios

Reduction of the base risk in a herd

Preventive trimming OR 0,66 Footbaths OR 0,9 Increase the access to pasture + 2 months Rubber covering of concrete floors OR 0,66 Base risk in a herd that trims cows twice a year vs. once: 0,16 x 0,6 = 0,10

”what if” in different herds:

• ”what if” milk yield level of the herd is higher?
• ”what if” conception rate is low in the herd?

Simulation procedure

• simulation over 10 years

evaluation of long term effects

• 500 replications

stochastic

• discard the first 5 years

”burn in” period

• results are the average of the last 5 years

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Results

Comparison of a low and high risk herd External validation: sensitivity analysis Effect of milk quota Effect of different (re)production levels in a herd Efficacy of preventive measures

Technical comparison of two herds:

high base risk (0,16) vs. low base risk (0,08) of lameness

Result BR 0,16 BR 0,08 Diff. Feed/cow, SFU 5599.7 5610.3 +10.6 * Replacement rate 43.36 43.04

• 0.32 *

Dead cows, % 3.87 3.43

• 0.44 *

Cases of lameness 28.97 14.84

• 14.13 *

Cow year 118.42 118.42 0.0 Milk/cow, ECM 8493.5 8531.5 +38.0 *

* Significant difference: p < 0.05

Economic comparison of two herds:

high base risk (0,16) vs. low base risk (0,08)

Result BR 0,16 BR 0,08 Diff.

Sale: Milk 2112.7 2122.8 +10.2 * x 1000 DKK Heifers 53.3 56.6 +3.4 * Total 2359.4 2372.5 +13.0 * Purchase: Feed, cows 838.2 840.2 +2.0 * x 1000 DKK Other costs 116.6 107.9

• 8.7 *

Total 1242.9 1235.8

• 7.1 *

Margin: Total x1000 DKK 1116.5 1136.6 +20.1 * Per cow 9429 9594 +165 * Per kg ECM 1.110 1.124 +0.015 *

Economic comparison of two herds:

high base risk (0,16) vs. low base risk (0,08)

Attribute costs to lameness:

• Difference in milk sale is DKK 10.200
• result of 14 cows less lame in ”low risk herd”
• 10.200/14 = DKK 730 milk loss per lame cow
• ”low risk herd” has lower replacement rate
• on average the cows are older
• average production per cow is higher (indirect effect of lower lameness inc.)

Economic comparison of two herds:

high base risk (0,16) vs. low base risk (0,08)

Attribute costs to lameness: Costs of premature culling

• Loss of future income
• Reduced sale of heifers
• Costs of raising replacement

Attribute costs to lameness: Reproduction

• Extra insemination
• Days open
• Calves per cow

External validation of the model:

Sensitivity of model to the input parameters

How sensitive is the outcome of the model to the setting of the input parameters

• reduced milk yield (RMY): 8,6%, based on literature studies
• lowest value in literature: 5,2%
• highest value in literature: 12%

Comparison of two herds (base risk 16% and 8%): With RMY of 12%: 202 DKK +23% With RMY of 8,6%: 165 DKK With RMY of 5,2%: 158 DKK

• 4%

Model is most sensitive to the setting of ”reduced milk yield”

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External validation of the model:

Sensitivity of model to the input parameters

Economic comparison of two herds:

Costs per case of lameness: DKK 1430 Situation without milk quota: Herd with high incidence of lameness: 1,006,035 Herd with low incidence of lameness: 1,010,870 +4800 Situation with milk quota: correct for amount of milk produced Costs per case of lameness: DKK 1036 Low incidence herd produces the same amount of milk, with fewer cows Why simulation without quota? Buying and selling quota interferes heavily with the economic results

Economic comparison of two herds:

Costs per case of lameness: DKK 1430 ”what if” ...the compared herds differ Milk yield potential is 30 kg vs. 34 kg ECM

DKK 1322

Milk yield potential is 38 kg

DKK 1455

Pregnancy chance is 40% vs. 50%

DKK 2065

Heat detection eff. is 40% vs. 50%

DKK 1661

Costs per case of lameness in different herds

Lower milk yield potential

DKK 1322: lowest

• margins are lower, in general

Lower pregnancy chance

DKK 2065: highest

• difference in margin devided by fewer cases of lameness
• increased days open > longer lactations > cows spend more time in

”tail of the lactation curve” (low risk): fewer cases!

1 2 3 4 5 6 7 8 9 10 11 12

months of lactation

25 20 15 10 5

Economic comparison preventive measures:

Difference between grazing and zero-grazing farms

Per cow year*

Zero grazing Grazing Lame cows* 33.3

• 4.2

Margin* 9,377 +51 Total margin 1,110,438 +6,075

• other aspects of grazing interfere with the results.
• Feeding of roughage vs. grazing
• Labour
• Other benificial effects on health
• ...

Economic comparison preventive measures:

Difference with the ’no prevention’ strategy in zero-grazing farms

Per cow year*

No prevention Rubber floor or trim twice Footbath Lame cows* 33.3

• 10.9

3.7 Margin* 9,377 +126 +44 Total margin 1,110,438 +14,781 +5,257

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Difference with the ’no prevention’ strategy in zero-grazing farms

No prevention Rubber floor or trim twice Footbath Total margin 1,110,438 +14,781 +5,257

Practical implications Footbath, twice a month, 24 per year: 5257/24: < 220 DKK per bath

• labour, products (e.g. CUSO4)

Trim twice vs. once: 120 cows, 6 per hour, 20h: labour<750 DKK

• who trims? Vet, trimmer, farmer (opportunity costs)

Rubber floors, last for 10 years (?): installation costs: <150.000 DKK

• faster growth of horn on rubber > trimming freq should increase as well

Economic comparison preventive measures:

Effect in herds with different base risks (incidence levels)

Cases of lameness

5 10 15 20 25 30 35 40

N

• p

r e v e n t i

• n

F

• t

b a t h B R x , 7 5 T r i m t w i c e B R x , 5 B R x , 2 5

cases of lameness

BR 0,20 BR 0,16 BR 0,08 BR 0,04

Economic comparison preventive measures:

Effect in herds with different base risks (incidence levels)

Margin Per Cow-Year

12900 13000 13100 13200 13300 13400

N

• p

r e v e n t i

• n

F

• t

b a t h B R x , 7 5 T r i m t w i c e B R x , 5 B R x , 2 5

DKK BR 0,20 BR 0,16 BR 0,08 BR 0,04

Economic comparison preventive measures:

Principle of economics of animal health

Optimization: not a feature of SimHerd

Markov decision processes and dynamic programming...

Discussion

• 1. Parameterisation

Lameness is a symptom of several diseases Causes of lameness were specified: e.g. digital dermatis 21%

• input parameters are result of weighted average
• preventive strategies only effective against certain diseases

”What if” assumption about the distribution wrong?

• ”what if” digital dermatitis (and interrelated diseases!!) cause

50% of the lameness cases?

• Economic effect of footbath doubles
• Economic effect of rubber flooring decreases

Discussion

• 2. Parameterisation: state of nature

Base risk of the standard cow to become lame: 0,16 Logistic regression model: cow specific probability Stochastic triggering of event: uncertainty in the occurence of it No representation of variation of parameters between herds

• 500 replications ≈ 500 ”different herds”
• no variation between these 500 different herds
• all herds have a base risk of 0,16
• biological uncertainty (between herds) is not represented

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Other discussion points

• 1. Common cow-level response
• 2. Common farmer response

(decisions, skills, opportunity costs)

Conclusions

• 1. Average costs of lameness in modern Danish dairy herd:

DKK 1430

• 2. Costs are about 28% lower in situation with quota
• 3. Costs depend on the herds milk yield level and

reproductive efficiency

• 4. The model is most sensitive to the parameter setting of

”reduced milk yield” and ”treatment costs” of lameness

Conclusions

• 5. Effect of rubber floors and trimming twice a year both

increase the margin per cow year with DKK 126

• 6. Effect of footbaths increases margin per cow year with

”only” DKK 44

• 7. Effect of preventive measures depends on the type of

lameness problem (infectious, metabolic...)

PhD project: 2005-2008

Tackling of important discussion points:

• 1. Lameness is a symptom of several diseases
• 2. Representation of biological uncertainty between farms
• 3. Use of herd specific ”evidence” to make the model

capable of herd specific decision support

PhD project: 2005-2008

Tackling of important discussion points:

• Lameness is a symptom of several diseases

type: skin hoof horn legs

• rigin:

infectious metabolic trauma stress risk factors: age production level, housing breed lactation stage season effects: milk production conception treatments

PhD project: 2005-2008

Tackling of important discussion points:

• Lameness is a symptom of several diseases

Digital dermatitis Interdigital hyperplasia Heel horn erosion Phlegmon Sole haemorrhage White line disease Sole ulcer

Metabolic origin Infectious origin High parity, high risk Low parity, high risk

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PhD project: 2005-2008

Tackling of important discussion points:

• 2. Representation of biological uncertainty between farms

1 P(123) = ---------------- 1+e-(β0+βpartiy) Simherd currently

• β0 =
• 1.66 (logit value of the base risk of 0.16)
• βparity =
• 0.59 for parity 1 vs parity 3 (OR of 0.56)
• 0.25 for parity 2 vs parity 3 (OR of 0.78)

0.22 for parity 4 vs parity 3 (OR of 1.25)

PhD project: 2005-2008

Tackling of important discussion points:

• 2. Representation of biological uncertainty between farms

1 P(123) = ---------------- 1+e-(β0+βpartiy) Simherd supplemented

• β0 =

(µ,σ2) e.g. (-1.66, 12)

• βparity =

1 vs 3 (µ,σ2) e.g. (-0.59, 0.52) 2 vs 3 (µ,σ2) e.g. (-0.25, 0.52) 4 vs 3 (µ,σ2) e.g. (-0.25, 0.52)

PhD project: 2005-2008

Simherd currently β0 =

• 1.66

Simherd supplemented β0 = (-1.66,12)

• 500 replications with a fixed value: 500 x simulation of the same farm
• 500 replications with a distribution: simulation of 500 ’different’ farms

Currently: 500 replications with fixed value: 500 runs with ”-1.66” After PhD: 500 replications with distribution: 500 draws from distribution

• 1,540

1st run

• 1,067
• 0,899

... +0.278

• 1,130

500st run

PhD project: 2005-2008

• 1,540

1st run

• 1,067
• 0,899

... +0.278

• 1,130

500st run

A state of nature drawn from the hyper distribution represents one (hypothetical) herd.

By drawing e.g. many states of nature we can generate many realistic hypothetical herds. Decision rules may have different effects in different herds.

The hyper distribution represents the whole population of herds under the conditions in question. Simherd supplemented β0 = (-1.66,12)

PhD project: 2005-2008

Use herd specific knowledge (evidence) to update the believe in the distribution The hyper distribution is created based on prior information about the parameter (prior distribution) Conditioned on herd specific observations (lameness prevalence) a posterior distribution is created More Bayesian later… Tackling of important discussion points:

• 3. Use of herd specific ”evidence” to make the model capable of herd

specific decision support

PhD project: 2005-2008

Prior distribution Posterior distribution Herd specific observations

• Evidence
• Belief

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Winbugs: Bayesian Analysis of complex statistical models using MCMC Prob Lame <-1-(1-Pr DD)*(1-Pr OID)*(1-Pr HHD) 1 Pr DD = ---------------------- 1+e-(β0+βpar2+βpar3) Obs Lame ~ Bern(Prob Lame) Lameness causing diseases DD: Digital Dermatitis OID: Other Interdigital Diseases HHD: Hoof Horn Diseases

0.21 0.96 0.12 0.23 0.19

• 0.16

βpar3 0.17 0.12 0.12 0.23 0.18 0.03 βpar2 0.35

• 2.09

0.32

• 0.88

0.25

• 1.27

β0 Posterior σ

σ

Prior Posterior σ

σ

Prior Posterior σ Prior σ HHD OID DD

Prior estimate: best guess before visiting the herd under study 1) Best guess of finding DD, OID and HHD in a large herd (>180 cows), zero-grazing Prob DD=0.22 Prob of finding a lame cow: 1-(1-0.22)*(1-0.29)*(1-0.11) = 0.51 Prob OID=0.29 Prob HHD=0.10 Data to condition the prior estimates on 2) In the herd under study 60 out of the 300 observed cows were diagnosed as lame Overall lameness prevalence: 20% parity 1: 10% parity 2: 20% parity 3: 30% 1 Pr DD = ---------------------- 1+e-(β0+βpar2+βpar3)

0.14 0.94 0.21 0.96 0.08 0.23 0.12 0.23 0.14

• 0.17

0.19

• 0.16

βpar3 0.11 0.10 0.17 0.12 0.08 0.20 0.12 0.23 0.12

• 0.02

0.18 0.03 βpar2 0.22

• 2.54

0.35

• 2.09

0.19

• 1.74

0.32

• 0.88

0.17

• 1.74

0.25

• 1.27

β0 Posterior σ

σ

Prior Posterior σ

σ

Prior Posterior σ Prior σ HHD OID DD

Prior estimate: best guess before visiting the herd under study 1) Best guess of finding DD, OID and HHD in a large herd (>180 cows), zero-grazing Prob DD=0.22 Prob of finding a lame cow: 1-(1-0.22)*(1-0.29)*(1-0.11) = 0.51 Prob OID=0.29 Prob HHD=0.10 Data to condition the prior estimates on 2) In the herd under study 60 out of the 300 observed cows were diagnosed as lame Overall lameness prevalence: 20% parity 1: 10% parity 2: 20% parity 3: 30%

0.14 0.94 0.21 0.96 0.08 0.23 0.12 0.23 0.14

• 0.17

0.19

• 0.16

βpar3 0.11 0.10 0.17 0.12 0.08 0.20 0.12 0.23 0.12

• 0.02

0.18 0.03 βpar2 0.22

• 2.54

0.35

• 2.09

0.19

• 1.74

0.32

• 0.88

0.17

• 1.74

0.25

• 1.27

β0 Posterior σ

σ

Prior Posterior σ

σ

Prior Posterior σ Prior σ HHD OID DD

2) Data to condition prior estimates on: 20% prevalence Posterior estimate: Prob DD=0.15 Prob of finding a lame cow: 1-(1-0.15)*(1-0.15)*(1-0.07) = 0.33 Prob OID=0.15 Prob HHD=0.07 Prior estimate: best guess before visiting the herd under study 1) Best guess of finding DD, OID and HHD in a large herd (>180 cows), zero-grazing Prob DD=0.22 Prob of finding a lame cow: 1-(1-0.22)*(1-0.29)*(1-0.11) = 0.51 Prob OID=0.29 Prob HHD=0.10

13 vs. 78 lameness cases Costs per case: €177 SE €3

5% 27%

15 vs. 129 lameness cases Costs per case: €170 SE €8

SD 0.5

Logit values P values

Logit (P) P value

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Distribution has ”biological” shape Maximum values are too extreme

MEAN 0.65 MEDIAN 0.55 MAXIMUM 3.0

PhD project: 2005-2008